Estimation of eect size posterior using model averaging over Bayesian network structures and parameters
Gábor Hullám, Péter Antal · 2012
Bayesian networks provide multiple advantages in feature subset analysis, but the parametric properties of Bayesian networks are typically neglected in inductive approaches, as they are focused on existential inference of relevant variables. However, in many application fields, particularly in biomedicine, certain parametric properties, such as eect size measures, are essential and widely used in interpretation, because they provide a more detailed characterization of relevance. To cope with multiple hypothesis testing, the Bayesian statistical framework became popular, but the posterior distribution of these eect size measures derived by Bayesian model averaging over structures are analytically not tractable, thus their estimation requires Monte Carlo simulation methods. In this paper we compare the structural (existential) and parametric (quantitative) concepts of Bayesian relevance and overview Bayesian approaches to the estimation of eect size posteriors. Furthermore, we compare the high probability density regions of these posteriors with traditional frequentist confidence intervals. Methods are illustrated on an artificial data set simulating a genetic association study.